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Comptes Rendus. Mathématique
Algebraic geometry
Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 483-489.

Let X be one of the 28 Atkin–Lehner quotients of a curve X 0 (N) such that X has genus 2 and its Jacobian variety J is absolutely simple. We show that the Shafarevich–Tate group Ш(J/) is trivial. This verifies the strong BSD conjecture for J.

Soit X un des 28 quotients d’Atkin–Lehner d’une courbe X 0 (N) tel que X est de genre 2 et sa jacobienne J est absolument simple. On démontre que le groupe de Shafarevich–Tate Ш(J/) est trivial. Ceci vérifie la conjecture BSD forte pour J.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.313
Classification: 11G40,  11-04,  11G10,  11G30,  14G35
Timo Keller 1; Michael Stoll 1

1 Lehrstuhl Mathematik II (Computeralgebra), Universität Bayreuth, Universitätsstraße 30, 95440 Bayreuth, Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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     title = {Exact verification of the strong {BSD} conjecture for some absolutely simple abelian surfaces},
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Timo Keller; Michael Stoll. Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 483-489. doi : 10.5802/crmath.313. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.313/

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